Spectrum sharing has attracted a lot of attention in cognitive radio recently as an effective method of alleviating the spectrum scarcity problem by allowing unlicensed users to coexist with licensed users under the condition of protecting the latter from harmful interference. In this paper, we focus on the throughput maximization of spectrum sharing cognitive radio networks and propose a novel cognitive radio system that significantly improves their achievable throughput. More specifically, we introduce a novel receiver and frame structure for spectrum sharing cognitive radio networks and study the problem of deriving the optimal power allocation strategy that maximizes the ergodic capacity of the proposed cognitive radio system under average transmit and interference power constraints. In addition, we study the outage capacity of the proposed cognitive radio system under various constraints that include average transmit and interference power constraints, and peak interference power constraints. Finally, we provide simulation results, in order to demonstrate the improved ergodic and outage throughput achieved by the proposed cognitive radio system compared to conventional spectrum sharing cognitive radio systems.